© BIS 2004

B U R E A U O F I N D I A N S T A N D A R D SMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

IS : 9456 - 1980(Reaffirmed 2003)

Edition 1.1(1982-03)

Price Group 7

Indian StandardCODE OF PRACTICE FOR

DESIGN AND CONSTRUCTION OFCONICAL AND HYPERBOLIC PARABOLOIDAL

TYPES OF SHELL FOUNDATIONS

(Incorporating Amendment No. 1)

UDC 624.15.023.62 : 624.04 : 006.76

IS : 9456 - 1980

© BIS 2004

BUREAU OF INDIAN STANDARDS

This publication is protected under the Indian Copyright Act (XIV of 1957) andreproduction in whole or in part by any means except with written permission of thepublisher shall be deemed to be an infringement of copyright under the said Act.

Indian StandardCODE OF PRACTICE FOR

DESIGN AND CONSTRUCTION OFCONICAL AND HYPERBOLIC PARABOLOIDAL

TYPES OF SHELL FOUNDATIONS

Foundation Engineering Sectional Committee, BDC 43

Chairman Representing

PROF DINESH MOHAN Central Building Research Institute (CSIR),Roorkee

Members

DR R. K. BHANDARI Central Building Research Institute (CSIR),Roorkee

CHIEF ENGINEER Calcutta Port Trust, CalcuttaSHRI S. GUHA ( Alternate )

SHRI K. N. DADINA In personal capacity ( P-820, Block P, NewAlipore, Calcutta )

SHRI M. G. DANDAVATE Concrete Association of India, BombaySHRI N. C. DUGGAL ( Alternate )

SHRI R. K. DAS GUPTA Simplex Concrete Piles (I) Pvt Ltd, CalcuttaSHRI H. GUHA BISWAS ( Alternate )

SHRI A. G. DASTIDAR In personal capacity ( 5, Hungerford Court, 121Hungerford Street, Calcutta )

SHRI V. C. DESHPANDE Pressure Piling Co (India) Ltd, BombayDIRECTOR (CSMRS) Central Water Commission, New Delhi

DEPUTY DIRECTOR (CSMRS) ( Alternate )SHRI A. H. DIVANJI Asia Foundation and Construction Pvt Ltd,

BombaySHRI A. N. JANGLE ( Alternate )

SHRI A. GOSHAL Braithwaite Burn & Jessop Construction Co Ltd,Calcutta

SHRI N. E. A. RAGHVAN ( Alternate )DR SHASHI K. GULHATI Indian Institute of Technology, New Delhi

DR A. VARADARJAN ( Alternate )SHRI M. IYENGAR Engineers India Limited, New Delhi

DR R. K. M. BHANDARI ( Alternate )SHRI G. S. JAIN G. S. Jain & Associates, Roorkee

SHRI ASHOK KUMAR JAIN ( Alternate )

( Continued on page 2 )

IS : 9456 - 1980

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( Continued from page 1 )Members Representing

JOINT DIRECTOR RESEARCH (SM) (RDSO)

Ministry of Railways

JOINT DIRECTOR RESEARCH(B & S) (RDSO) ( Alternate )

DR R. K. KATTI Indian Institute of Technology, BombaySHRI K. K. KHANNA National Buildings Organization, New Delhi

SHRI SUNIL BERRY ( Alternate )SHRI S. R. KULKARNI M. N. Dastur and Company Pvt Ltd, Calcutta

SHRI S. ROY ( Alternate )SHRI O. P. MALHOTRA B & R Branch, Public Works Department,

Government of Punjab, ChandigarhSHRI A. P. MATHUR Central Warehousing Corporation, New DelhiSHRI V. B. MATHUR Mchenzies Limited, BombaySHRI Y. V. NARASIMHA RAO Bokaro Steel Plant (Steel Authority of India)BRIG OMBIR SINGH Engineer-in-Chief’s Branch, Army Headquarters

MAJ H. K. BHUTANI ( Alternate )SHRI B. K. PANTHAKY Hindustan Construction Co Limited, Bombay

SHRI V. M. MADGE ( Alternate )SHRI M. R. PUNJA Cemindia Company Ltd, Bombay

SHRI S. MUKHERJEE ( Alternate )PRESIDENT Indian Geotechnical Society, New Delhi

SECRETARY ( Alternate )SHRI A. A. RAJU Steel Authority of India, New DelhiDR GOPAL RANJAN University of Roorkee, RoorkeeDR V. V. S. RAO Nagadi Consultants Pvt Ltd, New DelhiSHRI ARJUN RIJHSINGHANI Cement Corporation of India, New Delhi

SHRI O. S. SRIVASTAVA ( Alternate )DR A. SARGUNAN College of Engineering, Guindy, Madras

SHRI S. BOOMINATHAN ( Alternate )SHRI K. R. SAXENA Engineering Research Laboratories, Government

of Andhra Pradesh, HyderabadDR S. P. SHRIVASTAVA United Technical Consultants Pvt Ltd, New

DelhiDR R. KAPUR ( Alternate )

SHRI N. SIVAGURU Roads Wing, Ministry of Shipping and TransportSHRI D. V. SIKKA ( Alternate )

SHRI T. N. SUBBA RAO Gammon India Limited, BombaySHRI S. A. REDDI ( Alternate )

SUPERINTENDING E N G I N E E R (DESIGN)

Central Public Works Department, New Delhi

EXECUTIVE ENGINEER (DESIGN V) ( Alternate )SHRI M. D. TAMBEKAR Bombay Port Trust, BombaySHRI D. AJITHA SIMHA,

Director (Civ Engg)Director General, ISI ( Ex-officio Member )

SecretarySHRI K. M. MATHUR

Deputy Director (Civ Engg), ISI( Continued on page 29 )

IS : 9456 - 1980

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Indian StandardCODE OF PRACTICE FOR

DESIGN AND CONSTRUCTION OFCONICAL AND HYPERBOLIC PARABOLOIDAL

TYPES OF SHELL FOUNDATIONS

0. F O R E W O R D

0.1 This Indian Standard was adopted by the Indian StandardsInstitution on 18 March 1980, after the draft finalized by theFoundation Engineering Sectional Committee had been approved bythe Civil Engineering Division Council.

0.2 Shells are structures which derive their strength from ‘form’ ratherthan ‘mass’. The basic attribute of the shell which recommends its usein roofs is economy under conditions of large spans, apart fromaesthetics, which, of course, is of no concern in the case of a buriedstructure like the foundation. It has been found in respect offoundations that in situations involving heavy column loads to betransmitted to weaker soils, adoption of shells can lead to substantialsaving in concrete and steel.

0.2.1 Analysis has indicated that the economy with shell foundationsnormally increases with increase in column load and decreases inallowable bearing pressure of the soil, with greater sensitivity to thelatter.

0.2.2 Attendent on the saving in valuable materials of constructions, isthe fact that in all cases shell footings are substantially lighter thantheir plain counterparts. The attribute of lightness and the consequentease for transportation indicate high scope for precasting these shellfootings.

0.2.3 Since foundation shells bear directly on soil at their bottom andcarry backfill on top, besides being deep and thick, the problem ofelastic stability (buckling) is of lesser concern in foundation shells whencompared to roof shells. However, cracking of concrete is a subject ofgreater concern, as with all foundations, particularly under deleteriousground environments, for fear of corrosion of the reinforcing steel.Hence sufficient cover requirements and other preventive measures areindicated. It may be noted here that design based on membrane theoryusually results in nearly uncracked sections at working loads.

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0.3 Even though a variety of shells such as cylinder, cone hyperbolicparaboloid, elliptic paraboloid and inverted dome, and also funicularshells, can be judiciously adapted in various foundation situations, thisstandard covers only conical and hyperbolic paraboloidal shells; thesebeing of more frequent use in foundations.0.3.1 Between cone and ‘hypar’ (common abbreviation for hyperbolicparaboloid), however, while the use of the former is limited toindividual footings on account of its circular plan, the latter can beadopted for individual footings (square or rectangular), combinedfootings as well as for rafts.0.4 The depth, thickness and boundary, as well as loading conditions offoundation shells are such that rigorous analyses involving them arenecessarily much more complex than those of roof shells. The state ofstress in foundation shells can be predicted to any reasonably high degreeof accuracy only by a rigorous ‘bending analysis’ involving the abovefactors. Such an analysis being not easily amenable to practical use, thedesign of foundation shells is usually made on the basis of the muchsimpler. ‘membrane analysis’, which is based on a large number ofradically simplifying assumptions with regard to the factors mentionedabove. The membrane analysis is invariably a conservative design aid,and the approach to design based on it, with necessary modifications inthe matter of detailing which will ensure the high ultimate strength (loadcarrying capacity) of these foundations, has been found to be sufficientfor all practical purposes. Hence the same is recommended in this code.

NOTE — The provisions given in this standard have been explained in detail in thebook ‘Modern Foundation — An Introduction to Advanced Techniques: Part I ShellFoundation’ by Dr Nainan P. Kurian.

0.5 This edition 1.1 incorporates Amendment No. 1 (March 1982). Sidebar indicates modification of the text as the result of incorporation ofthe amendment.0.6 For the purpose of deciding whether a particular requirement ofthis standard is complied with, the final value, observed or calculated,expressing the result of a test or analysis, shall be rounded off inaccordance with IS : 2-1960*. The number of significant placesretained in the rounded off value should be the same as that of thespecified value in this standard.

1. SCOPE

1.1 This standard covers the design and construction aspectspertaining to conical and hyperbolic paraboloidal types of shellfoundations subjected to the action of isolated column loads.

*Rules for rounding off numerical values ( revised ).

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2. TERMINOLOGY

2.1 For the purpose of this standard the definitions given inIS : 1904-1978*, IS : 6403-1971†, IS : 2210-1962‡, IS : 2204-1962§, andthe following shall apply.

2.1.1 Shell Foundation — Foundations which incorporate structuralshell elements in place of the plain element of ordinary shallowfoundations.

3. NECESSARY INFORMATION

3.1 The information called as in IS : 1080-1962|| and IS : 2950(Part I)-1973¶ are required for the purpose of this code. The additionalinformation as indicated in 3.1.1 will also be necessary.

3.1.1 Suitability of In-situ Soil for Core Preparation ( see Fig. 1 and 3 )Under Shell Foundations — If in-situ soil is shrinkable, necessity forbringing non-swelling soil from elsewhere for this purpose is indicated.(This is necessary to allay the fear of partial loading of the shellbrought about by a variable subsidence of the core soil).

4. PRELIMINARY DESIGN CONSIDERATIONS

4.0 The complete design of a shell foundation, consists of two parts,namely, ‘soil design’ and ‘structural design’.

4.1 The aim of soil design is to proportion the foundation (that is, todetermine its plan dimensions) so that the ‘net loading intensity’ ( seeIS : 6403-1971† ) under actual field conditions does not exceed the‘allowable bearing pressure’ ( see IS : 6403-1971† ), which is the lesserof (a) the ‘safe net unit bearing capacity’, and (b) soil pressure for agiven permissible settlement. It may be noted in this connection thatin case of sand the safe net unit bearing capacity increases and soilpressure for a given settlement decreases with increase in thefoundation width, unlike the case of clay where the safe net unitbearing capacity is independent of the foundation dimensions.

NOTE — Width is the smaller of the plan dimensions, which alone influences thesequantities.

*Code of practice for structural safety of buildings : shallow foundations ( secondrevision ).

†Code of practice for determination of allowable bearing pressure on shallowfoundations.

‡Criteria for the design of reinforced concrete shell structures and folded plates.§Code of practice for construction of reinforced concrete shell roof.||Code of practice for design and construction of simple spread foundations.¶Code of practice for design and construction of raft foundations: Part I Design

( first revision ).

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FIG. 1 PLAN SHOWING REINFORCEMENT OF CONICAL FOOTING

FIG. 2 CONICAL SUBSTRUCTURE FOR TOWERS

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4.2 The net loading intensity and the allowable bearing pressureshould be determined according to IS : 6403-1971*. The influence ofthe position of water-table on these quantities should be carefullyascertained and duly taken into acount.

4.3 If the soil filling the hollow space underneath the shells (core)( see Fig. 1 ) is assumed to be incompressible and act integrally withthe foundation, the soil response below the shell foundation in terms ofboth bearing capacity and settlement will be modified to the extent of

FIG. 3 HYPERBOLIC PARABOLOIDAL SHELL FOOTING

*Code of practice for determination of allowable bearing pressure on shallowfoundations.

IS : 9456 - 1980

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the additional friction that will be mobilized at the bottom of thetrench between soil and soil, than at the interface between foundationand soil as in the case of plain foundations. However, results of limitednumber of tests tend to indicate that this variation in soil response ismarginal. Hence it is customary to ignore this difference and assumethe bearing capacity and settlement under shell and plain foundationsto be identical, under identical foundation conditions, for the purposeof soil design.

5. STRUCTURAL DESIGN

5.0 The structral design of the foundation should follow afterproportioning the foundations in accordance with the requirements setout in 4.5.1 The conical footing shown in Fig. 1 is the simplest form in which ashell is made use of in foundation. The provision of radial and circum-ferential steel is as simple as for a circular plain raft (footing) whilethe construction is only a little more difficult.

NOTE — While this type of conical foundation is potentially suited for individualcolumns, chimney stacks and similar tower shaped structures, the majority ofinstances in which these shells have been adopted are for tall telecommunicationtowers (television, radio, telephone, etc) in reinforced concrete, where they serve notas regular foundations, but as substructures linking the tower shaft to the annularraft, or ring which is regular foundation bearing on soil ( see Fig. 2 ). The space withinthis conical substructure is utilized for services. Very often these cones are stiffenedinternally, the stiffening taking various forms, to resist moments and shears due towind effects, etc. Prestressing is indicated for the hoop reinforcement in the cone aswell as the foundation ring, to prevent or limit the width of cracks in concrete. Theseconical shells being substructures, are beyond the scope of this standard.

5.2 While the cone is a singly curved shell, the hyperbolic paraboloid isa doubly curved anticlastic shell with its surface made up of two sets ofparabolae having curvatures in opposite directions. The chief advantageof the hypar, however, is that just as the cone, it is also a ruled surface,( see Appendix A of IS : 2210-1962* for shell classification) consisting oftwo sets of straight line generators inclined at 45° to the parabolae, asshown in Fig. 3.5.2.1 This straight line property of the cone and hyperbolic paraboloidare effectively exploited in profiling the core soil and the shell, besidespreparing the reinforcement grills, and formwork for making precastshell footings.5.2.2 The combination of hypar shell elements (square or rectangular)with set of edge and ridge beams shown in Fig. 3, is popularly knownas the ‘umbrella’ footing, it being the natural offshoot of the wellknown ‘inverted umbrella’ shell used in the construction of roofs.

*Criteria for the design of reinforced concrete shell structures and folded plates.

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5.3 In the dimensioning of the shell foundations, the ratio of rise tobase radius ( f/r2 ) in the case of cone ( see Fig. 1 ), and the rise to baseratio of the shell ( f/a ) in the case of hyperbolic paraboloid ( see Fig. 3 ),shall vary from 0.5 to 1. From the point of view of ease of construction,values near the lower limit are more suitable. It may, however, benoted that membrane theory will not be adequate for design at verylow values of rise.

5.4 The bottom rig beam in the case of cone and the edge and ridgebeams in the case of hyperbolic paraboloid are to be provided withinthe shell dimension as shown in Fig. 1 and Fig. 3 respectively, so as tokeep the plan dimensions arrived at by soil design intact.

5.4.1 In the case of the cone, the ring beams at the bottom are found tocontribute to the stiffness of the footing at lower rises ( f/r2 < 0.5 ),without any marked contribution at higher rises.

5.4.2 In the case of hyperbolic paraboloid, footings have been designedwithout ridge beams but with thick edge beams, and alternatively,with heavy ridge beams but without any edge beams. However,footings with both edge and ridge beams should be able to adaptthemselves better to irregular distribution of soil reaction andaccidental eccentricities in load that are bound to occur in practice. Assuch footings of this kind are to be recommended in normal cases.

5.4.3 As far as the positioning of the beams is concerned, downstandingbeams as shown in Fig. 3 are preferred as they are easier to constructand structurally more efficient from the point of view of possible bending.

5.4.4 When feasible, the width of the ridge beam may be made equal tothe width of the column base ( see Fig. 3 ). Where possible, in place ofthe projecting ridge beams, it may be more expedient, from the point ofview of construction both by in-situ and precast methods, and alsoeconomy to provide triangular ribs at the ridge, with its risedecreasing from a maximum at the column and vanishing at the jointwith edge beams.

5.4.5 The ring beam in the case of the cone and edge beams in the caseof hyperbolic paraboloid, in addition to improving the stiffness, delaycracking of the shell and also contribute substantially to the ultimateload carrying capacity of these foundations by providing substantialreserve of strength, leading thereby to higher load factors. From the pointof view of cracking, strong scope also exists for prestressing these beams.

5.5 Where cover requirements, and not stresses, govern thefoundation, shell shall have a minimum thickness of 15 cm. (In precastconstruction this can be reduced to 12 cm.)

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5.6 On the basis of the assumption that the weight of the core, mudmat, backfill and the self weight of the shell foundation, are directlytransmitted to the soil below in such a manner as will not induce anysubstantial stresses in the shell foundation, the structural design ofthe shell foundation may be carried out for the maximum loadtransmitted at the foot of the column to the foundation, as done inrespect of ordinary plain foundations.5.7 When the above load is divided by the plan area of the foundation( Ap ) which has been already finalized at the end of the ‘soil design’

( see 4 ), the average intensity of the soil pressure for the

structural design of the footing, is obtained. This pressure may beassumed to be uniform for the purpose of structural design.5.8 At every point of contact between the shell (and also beams) and soil,the soil reaction or ‘contact pressure’ can have normal and tangentialcomponents. The distribution of the actual resultant contact pressure ishighly indeterminate, because of the elastic nature of the soil support,and the complex shell-beam-soil interaction. In the case of soft clay whereno tangential frictional contact pressure components can be sustainedbecause. of the negligible wall friction, the resultant soil pressure maybe taken to be normal to the shell. However, in the case of sand, sincetangential pressures of considerable magnitude can be mobilized due tothe availability of higher contact friction, the resultant contact pressurecan show a substantial shift from the normal to the vertical. As a generalrule, it may be safer to design for the condition giving rise to higherstresses in each case. It may be noted in this connection that the intensityof the normal contact pressure (when tangential components are absent)is also obtained as P/AP if the latter is also assumed to be uniform, whichis the same as pv, the intensity of vertical pressure, where Ap is theprojected area of the foundation in plan ( see also Appendix A ).5.9 Under a uniform contact pressure, normal or vertical, the conicalshell is subjected to hoop tension decreasing upwards from amaximum at the base and a meridional compression decreasingdownwards from a maximum at top ( see Appendix A ). Hoop steel is tobe provided to take up the full tension, with preferably varyingspacing, to match the variation in hoop tension. The horizontalsections which are in compression may be designed as short columnswith steel not exceeding 5 percent. The steel so designed should beplaced at the middle plan of the shell. It may further be ensured thatsections are provided with minimum nominal steel of 0.5 percent.5.9.1 The thickness of the cone may be varied from a maximum at thetop to a minimum at the bottom. The maximum tensile hoop stress in

pvPAp-------=

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the equivalent concrete section may be checked according toIS : 456-1978* and the thickness finalized ( see 5.5 ).5.9.2 The ring beam at the bottom of the cone is optional. However,when the frustrum of a cone is used as foundation for a tower shaft, aring beam at the top is essential to balance the horizontal componentof the meridional compression at the top edge of the cone, whichproduces hoop compression in the latter.5.9.3 The cracking strength of the above membrane design is normallyhigher than the load given by the membrane theory. The ultimatestrength may be worked out by any suitable theory ( see Appendix A )and the load factor ascertained. It may be mentioned here that withthe onset of peripheral cracking, the soil pressure shows a tendency forshift from edges to the centre, which incidentally helps to increase theultimate strength.5.9.4 A cone may also be used in the inverted position as foundation forstructures such as guyed masts ( see Fig 4 ). In this case the loading(soil pressure) on the cone reverses sign subjecting the cone tomeridional tension and hoop compression. Use of cone in this mannerhas the disadvantage of heavy meridional tension, for design, at thebottom sections of the cone.

5.10 The hypar footing shown in Fig. 3 is designed on the basis of themembrane theory used in the design of the corresponding invertedumbrella roof. According to this theory, under a uniform vertical soilpressure, the shell membrane is subjected to a state of pure shear ofconstant magnitude unaccompanied by normal stresses. Thismembrane shear, produces tension and compression of equivalentmagnitude as the shear along the diagonally orthogonal convex andconcave parabolic arches respectively ( see Appendix A ). Since thedesign of the shell is governed by this tension, the full requirementthereof is to be provided in terms of steel. However to avoid the

*Code of practice for plain and reinforced concrete ( third revision ).

FIG. 4 INVERTED CONE AS FOUNDATIONFOR GUYED MAST

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necessity of bending bars to different parabolic profiles, it will be moreexpedient from the point of view of facility of grilwork, to detail thesteel in the shell as straight rods along directions parallel to the edgesin such a manner that its effective area along the diagonal is sufficientto withstand the full tension. Since this arrangement produces thesame effective steel along the directions of the compressive arches also,the presence of concrete makes the compressive arches also strongerthan the tensile arches, thereby leading to a slightly unbalanced, butat the sametime, safer design. It may be ensured that the steel thusprovided does not fall below a value of 0.5 percent. According to themembrane theory, this steel should lie at the middle plane of the shell.In most instances concrete will be needed only as a cover for steel.Checking the tensile stress in the equivalent concrete section inaccordance with IS : 456-1978* will usually reveal very low stresses,thereby ensuring practically uncracked sections at working loads.5.10.1 According to the membrane theory, the edge beams are subjectedto uniformly varying tension with zero value at corners and maximumvalue at the centres of edges ( see Appendix A ). Therefore, these centralsections may be designed on the same lines as the shell. The section ofthe edge beam may be determined on the basis of limiting tensionaccording to IS : 456-1978* and the edge steel detailed ensuring propercover requirements. Notwithstanding the reduction in tension, however,the same section is normally provided throughout the edge. As far as theridge beams are concerned, they are subjected to axial compression withzero value at the base and maximum value at the apex ( seeAppendix A ). The section of the ridge beam may be designed as a shortcolumn with steel not exceeding 5 percent and detailed ensuring propercover requirements. Irrespective of the variation in compression, thesame section may be provided throughout the ridge as done in the caseof edge beams. The design is complete with stirrups (nominal accordingto membrane theory) provided both in the ridge and edge beams.5.10.2 Further detailing practices necessary to ensure the full ultimatestrength of the hypar foundation are given in Appendix B.5.10.3 Footings designed on the above lines crack at loads higher thanthose given by the membrane theory. The full ultimate strength of thefooting may be determined by a suitable theory ( see Appendix A ) forascertaining the load factor.5.11 Since hyperbolic paraboloidal combined footings and rafts (Fig. 5and 6) are essensially multiple units of the individual footing, theseare designed on the same basis, except that valley beams which are

*Code of practice for plain and reinforced concrete ( third revision ).

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edge beams common to two shells on either side, should be designed forthe combined tension. Depending upon the area requirement of thefoundation (soil design), the spacing of the columns, and the differencein column loads, different sets of square or rectangular shells willresult in the design. The same applies to individual rectangularfootings ( see Fig. 7 ). However, where the column loads are unequal, itwill be profitable to ensure that the resultant column load passesthrough the centre of gravity of the area of contact between thefoundation and the soil in plan, so that the soil pressure on thefoundation will be uniform throughout.

5.11.1 Where soil conditions permit (in terms of the requirements onplan area), the inverted hipped hyperbolic paraboloid ( see Fig. 8 )normally used in roofs, may suggest itself as a possible alternative foruse as foundation. While this combination has the structuraladvantage that both the sets of beams are in compression,notwithstanding the necessity for tie beams between columns, its chiefdrawback in foundation is the difficulty of providing effective soilsupport below the triangular edges. Hence this type cannot berecommended for foundations in normal cases.

FIG. 5 COMBINED HYPAR FOOTING

FIG. 6 HYPAR RAFT

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5.12 As with other foundations, shell foundations also may be calledupon to resist horizontal loads and moments at the level of its base, asa result of horizontal loads or couples or both transmitted from aboveor due to eccentricities of column loads. As for horizontal loads, shellfoundations have the advantage of higher capacities to the extent ofthe increased friction (soil to soil contact) at the base even though itsself-weight may be less than that of its plain counterpart. As regardsmoments, the same may be treated as in the case of plain foundations,as resulting in a linearly varying soil pressure distribution. Undersuch circumstances, the individual shell elements may be designed forthe maximum soil pressure occurring under it due to the combinedeffect of vertical load and moment, to be on the safer side. However,where membrane solutions are available for the anti-symmetrical soilpressure produced by moment the stress resultants the latter may besuperimposed on the stress resultants produced by the symmetricalsoil pressure due to the vertical load for the purpose of the designs.

FIG. 7 RECTANGULAR HYPAR FOOTING

FIG. 8 INVERTED HIPPED HYPERBOLIC PARABOLOIDAL RAFT

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6. CONSTRUCTION

6.1 The concrete for shell foundations should be of grade not less thanM20.

6.2 Shell foundations may be cast in-situ or precast. Even though thesefoundations are generally laid in-situ, the advantages of the shell interms of lightness and transportability is best exploited in precasting.Because of this basic attribute of lightness, it should be noted that evenlarge-sized footings of this kind are amenable to precasting. To this mustbe added the possibility of higher strength for the same mix ( see 6.1 ) onaccount of the better control that can be exercised during prefabrication.

6.3 In the in-situ method of construction, the shell foundation is cast atsite on the soil core which has been cut to the correct profile of theshell. The straight line property of the shell enables this profiling to besimply achieved by rotating a template about a central axis in the caseof the cone ( see Fig. 9 ), and by moving a straight edge afterestablishing the ridge and base lines in the case of the hyperbolicparaboloid ( see Fig. 10 ). A thin layer of lean cement mortar (mix nothigher than 1 : 3) is then placed over the soil core ( see Fig. 11 ). This isdone to facilitate grillwork (bending and tying of reinforcements) andsubsequent casting. Even when the foundations are moderately steep,formwork is needed only at the edges.

6.3.1 In the case of expansive soils, the core on which the footing is tobe laid, should be prepared by cutting a trench to level bottom andfilling it with non-swelling, or if possible with stabilized, soil. The soilis then compacted and profiled as described in 6.3 ( see Fig. 12 ). Thiswill prevent the chances of subsidence of the core brought about by apossible shrinkage. At any rate this will give rise to conditions at thebase level of the shell foundation similar to those under plainfoundation. To this must be added precautions normally taken inrespect of plain shallow foundations in shrinkable soils.

FIG. 9 CORE PROFILING FOR CONE

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FIG. 10 CORE PROFILING FOR HYPAR

FIG. 11 In-situ CONSTRUCTION (SECTION ALONG DIAGONAL)

FIG. 12 In-situ CONSTRUCTION ON STABILIZED SOIL CORE(SECTION ALONG DIAGONAL)

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6.3.2 In any case, whether the construction is in-situ or precast, it isvery important to ensure that there is no loss of contact anywherebetween the footing and the soil, since partial contact will lead toconcentration of loads (soil pressure) on the shell, which can vitiate theperformance of the shell itself, and precipitate premature collapse.6.4 Precast cone and hypar footings may be cast in inverted woodenmould which helps easier removal of the footing from the mouldfacilitated by shrinkage. The moulds may be easily formed by cuttingand nailing plywood strips along the directions of the straight linegenerators into a frame ( see Fig. 13 ). An alternative technique whichmay be simpler and certainly more advantageous in terms of thenumber of units that can be turned out from each mould would be tomake a mould in concrete itself ( see Fig. 14 ). This can be done bymaking a box with wooden sides to conform to the edges and filling, theinside with lean concrete, profiling the same by template or straightedge as the case may be and finishing it smooth with cement paste.6.4.1 In precast construction, however, it will not be expedient to out thesoil to the required profile first as done in the case of in-situ construc-tion, and then place the footings on it, since in doing so full contactbetween the footing and the soil core cannot be ensured under allcircumstances. Instead, it would be more expedient to install theprecast footing in a trench cut to level bottom. After centering andlevelling the footing, dry sand may be poured into the hollow spacebelow the footing through a hole in the column base provided at the timeof casting. The sand thus poured is to be compacted to high and uniformdensities. In the case of steep conical footings this space is accessible forcompaction by manual tamping through the hole. However, in the case

FIG 13 MOULD FOR HYPAR

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of shallow conical footings, and hypar footings whose corners aresubstantially flat and therefore inaccessible even when the shells aredeep, this sand is to be compacted by some remote technique, so as toform a sound core under the shell to receive the load. Such a simple buthighly efficient technique of remote compaction is described inAppendix C. For connections with steel columns, bolts may be embeddedin the column base at the time of casting which will engage the holes inthe base plate of the column ( see Fig. 15 ). Incorporation of a neoprenepad between steel column and base plate will serve as a hingepreventing the transmission of any moment to the footing. Connectionwith concrete columns may be effected through dowels protruding fromthe column base for continuous casting, or a socket arrangement in thecolumn base into which a precast column is grouted as shown in Fig. 16.

FIG. 14 INVERTED CONCRETE MOULD FOR CONE

FIG. 15 FIXING OF STEEL COLUMN TO PRECAST HYPAR FOOTING

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A P P E N D I X A( Clauses 5.8, 5.9, 5.9.3, 5.10, 5.10.1 and 5.10.3 )

FORMULAE FOR THE DESIGN OF CONICAL AND HYPERBOLIC PARABOLOIDAL SHELL FOUNDATIONS

A-1. CONE

A-1.1 Membrane stress resultants per unit width of the shell due tovertical load and moment, are given below.

A-1.1.1 Stress Resultants Under Vertical Soil Pressure ( see Fig. 17 )

where pv is the intensity of vertical soil pressure

FIG. 16 SOCKET CONNECTION FOR R C COLUMN WITH PRECASTHYPAR FOOTING

Nθ =

= 0

, where P = column load, and

Ap = plan area of the footing(= π s2

2 sin2 α for full cone)

Nrpv2s------ α tan s2 s 2

2–( )=

pvs sin3α

cos α---------------

Nrθ

pvPAp-------=

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A-1.1.2 Stress Resultants Under Normal Soil Pressure ( see Fig. 17 )

where pn is the intensity of normal soil pressure, and P/Ap is sameas given under A-1.1.1.

The variation of the above stress resultants with the ratio of rise tobase radius ( f/r2 ) is shown in Fig. 18.

FIG. 17 MEMBRANE STRESS RESULTANTS IN CONICAL FOOTING

Nθ = pn s tan α

Nrθ = 0

FIG. 18 VARIATION OF Nθ AND Nr WITH f/r2 RATIO

Nrpn

′

2s------ α [ s2

2 s2– ]tan=

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21

A-1.1.3 Stress Resultants Under Anti-symmetrical Soil Pressure Due toMoment Assuming the Soil Pressure to be Normal ( see Fig. 19 )

in which , where M is the moment producing the

maximum anti-symmetrical soil pressure .

=

=

FIG. 19 CONICAL FOOTING UNDER MOMENT

N′r

2pn′

s2 2 αsin----------------------------

s24 s4

–

4 s2--------------------

s23 s3

–

3 s-------------------- α2

cos– θcos=

N′θ

pn′

s2------ s2 αtan θcos

N′rθ

pn′

4 s2 s2-------------------

s24 s4

–( )αcos

------------------------ θsin

pn′ 4 M

π s23 α3sin

--------------------------------=

pn′

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22

A-1.2 The ultimate strength (value of soil pressure at which thefooting fails structurally) Pu for uniform normal soil pressure, underassumptions of fixity at the upper edge, and a lower edge which iseither free or provided with a ring beam, and assuming constantspacing of hoop steel, are given in A-1.2.1 to A-1.2.2 ( see also Fig. 20 ).

A-1.2.1 Ultimate Normal Soil Pressure for Fixed Upper Edge and FreeLower Edge

where

A-1.2.2 Ultimate Normal Soil Pressure for Lower Edge With Ring Beam

where Nb = ultimate capacity of the ring beam in direct tension

FIG. 20 ULTIMATE FAILURE OF CONICAL FOOTING

N = ultimate capacity of the shell per unit width in directtension in the hoop direction (constant),

Ro = ,where ro is the radius corresponding to thelocation of the plastic hinge.

M = moment capacity of the plastic hinge per unit width( ro may be taken r1 for all practical purposes ).

pnu 6

αcos2

------------- 1 Ro–( )2 M α2sinN r2

----------------------- Ro+

Ro3 3 Ro 2+–

-------------------------------------------------------------------------------- Nr2-----=

ror2-----

pnu 6 N αcos 1 Ro–( )2

2 r2 Ro3 3 Ro 2+–( )

-------------------------------------------------------- + M 2 αsin

r22

------------------------- Ro

Ro3 3Ro 2+–

------------------------------------

+ Nb α cos αsin 1 Ro–( )

r22 R( o

3 3 Ro 2 )+–

------------------------------------------------------------------

=

Pu pnu Ap×=

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23

A-2. HYPERBOLIC PARABOLOIDA-2.1 The membrane stress resultants per unit width of the shellagainst vertical and normal soil reactions, together with the forces inbeams, are given below ( see Fig. 21 )

A-2.1.1 Stress Resultants Under Vertical Soil Pressure

( Nx, Ny and Nxy are the membrane stress resultants. ‘t’ is theequivalent tension per unit width developing in the convex parabolae ).

where, k = f /ab in which a and b are the plan dimensions of therectangular hyperbolic paraboloidal shell quadrant

( ‘k’ is called ‘warp’ of the shell ).For a square shell ( a = b )

k = f/a2

For the square hypar footing, T = t . awhere T is the maximum direct tension in the edge beam, at the

centre, and

where C is the maximum direct compression in the ridge beam, atthe apex.

FIG. 21 MEMBRANE STRESSES IN HYPAR FOOTING

Nx Ny 0= =

Nxy tpV2k-------= =

C 2t a2 f2+=

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24

A-2.1.2 Stress Resultants Under Normal Soil Pressure

where

( Nx and Ny are tensile )

T and C are obtained as before.A-2.2 Rigorous and simplified expressions for the ultimate strength Pu(column load at failure) of square hypar footings under vertical soilpressure for both ‘ridge’ and ‘diagonal’ failures are given in A-2.2.1and A-2.2.2 ( see Fig. 22 ).

z = k.x y, is the co-ordinate of the point ( see Fig. 21 ).[ Nx and Ny are tensile ]

Nxy =

where u =

and v =

Nxy = t =

FIG. 22 FAILURE MECHANISMS OF HYPAR FOOTING — Contd.

Nx 2 pn z 1 k2y2+

1 k2x2+------------------------=

Ny 2 pn z 1 k2x2+

1 k2y2+------------------------=

pn2k------- . 1 k2x2 k2y2 + +( )

1 k2⁄ y2+

1 k2⁄ x2+

pn2k------- 1 k2x2 k2y2+ +

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25

A-2.2.1 Diagonal Failure

where

A simplified form of the above expression which is sufficient for allpractical purposes is:

FIG. 22 FAILURE MECHANISMS OF HYPAR FOOTING

N = the ultimate tensile capacity of the shell section perunit width,

Nb = ultimate tensile capacity of the edge beam, and

Mr = ultimate moment capacity of the ridge section.

Pu 12 Nf af--- 1

2--- a

f---

3+

fa---

e

log 1 fa---

2++

=

12--- a

f---

3 fa--- 1 f

a---

2+×

12 Nb fa--- 6

Mra

--------+ +–

Pu 8 Nf 12 Nb fa---

6Mra

--------+ +=

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26

A-2.2.2 Ridge Failure — The corresponding simplified expression forultimate strength by ridge failure is:

where is the ultimate moment capacity of the failing ridgesection.

A P P E N D I X B( Clause 5.10.2 )

DETAILING OF REINFORCEMENT AT CRITICAL SECTIONS OF THE HYPERBOLIC PARABOLOIDAL FOOTING TO

ENSURE ITS FULL ULTIMATE STRENGTH

B-1. DETAILING

B-1.0 The critical sections of the hypar footing shown in Fig. 23 shallbe detailed as given in B-1.1 to B-1.3 which will substantially ensurethe development of its full ultimate strength.

B-1.1 Centres of Edge Beams — In the interest of preventing aridge failure, and ensuring ultimate strength by diagonal failure, theridge steel may be continued into the edge beams, bending in oppositedirections and properly anchored with hooks, as shown in Fig. 24A.The total percentage of steel in the central section of the edge beam,including such steel, shall not exceed 5 percent.

FIG. 23 CRITICAL SECTIONS OF HYPAR FOOTING

Pu 4 Nf 8 Nb fa---

82

------- M′r

a---------+ +=

M′r

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27

B-1.2 Corners of Edge Beams — To realise the full reserve strengthfrom the edge beam in diagonal failure, the corners may bestrengthened by extra diagonal steel properly anchored into fillets asshown in Fig. 24B.

B-1.3 Column Base-Ridge Joint — Even though the chances offailure of column by punching shear are remote on account of thetransmission of column load to the ridge beams essentially in directcompression, as an extra measure of precaution against column shear,fillets may be provided at the column base-ridge joint, as shown inFig. 24C, particularly where triangular ribs alone are providedwithout the projecting ridge beams.

A P P E N D I X C( Clause 6.4.1 )

REMOTE TECHNIQUE FOR INFILLING PRECASTSHELL FOOTINGS

This technique is called ‘Centrifugal Blast Compaction’ and iseffected by means of a centrifugal vane rotor, consisting of a rotatingspindle carrying falling blades, designed as a simple attachment to anordinary needle vibrator used for compacting concrete.

In this technique of compaction, after pouring a batch of dry sandthe rotor is inserted into the hollow space through the hole in the

FIG. 24 EXTRA PROVISIONS AT CRITICAL SECTIONS(ORIGINAL REINFORCEMENT NOT SHOWN)

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28

column base ( see Fig. 25 ). When the motor is, switched on, the vanesopen out automatically due to centrifugal action and start rotating athigh speeds. This high speed rotation of the vanes creates a heavyblast in the hollow space, under the influence of which, the sandparticles become quickly air-borne and start moving radially outwardswith high velocities. These particles collide against the inner surfacesof the footing, collapse and settle down to positions of maximumdensity due to the blast. As this process continues, the entire spacegets progressively filled up from the periphery inwards. The work canbe stopped on reaching the central portion which is directly accessiblefor manual compaction through the hole. Density indices (relativedensity) of the order of 80 to 90 percent can be obtained by thistechnique of compaction.

FIG. 25 CORE PREPARATION BY CENTRIFUGAL BLAST COMPACTION

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29

( Continued from page 2 )

Miscellaneous Foundation Subcommittee, BDC 43 : 6

Convener Representing

SHRI SHITALA SHARAN Public Works Department, Government of UttarPradesh, Lucknow

Members

SHRI E. T. ANITA Concrete Association of India, Bombay

SHRI N. C. DUGGAL ( Alternate )

SHRI S. P. CHAKRABARTI Indian Roads Congress, New Delhi

CHIEF ENGINEER (ROADS) Roads Wing (Ministry of Shipping and Transport),New Delhi

DIRECTOR Highways Research Laboratory, Madras

DEPUTY DIRECTOR RESEARCH/FE-II

Ministry of Railways ( RDSO), Lucknow

DEPUTY DIRECTOR STANDARDS(B & S) ( Alternate )

SHRI B. K. PANTHAKY Hindustan Construction Co Ltd, Bombay

SHRI P. G. RAMAKRISHNAN Engineering Construction Corporation Limited,Madras

SHRI G. B. SINGH ( Alternate )

SHRI S. A. REDDY Gammon India Limited, Bombay

SHRI G. R. HARIDAS ( Alternate )

SHRI ARJUN RIJHSINGHANI Cement Corporation of India, New Delhi

SHRI O. S. SRIVASTAVA ( Alternate )

DR SANKARAN Indian Institute of Technology, Madras

SHRI D. SHARMA Central Building Research Institute (CSIR),Roorkee

SHRI AMAR SINGH ( Alternate )

SUPERINTENDING E N G I N E E R (PLANNING CIRCLE)

Public Works Department, Government of WestBengal, Calcutta

Ad hoc Panel for Preparation of Code of Practice for Designand Construction of Conical and Hyperbolic Paraboloidal

Types of Shell Foundations, BDC 43 : 6 : 2

Member

DR NAINAN P. KURIAN Indian Institute of Technology, Madras

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Amendments Issued Since Publication

Amend No. Date of IssueAmd. No. 1 March 1982

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